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Table 4 Values choosing \(u^{1}(t)=\frac{1}{1+x\sin x}\) and \(v^{1}(t)=\exp ( t)\)

From: Iterative algorithms for solutions of Hammerstein equations in real Banach spaces

 

Algorithm (1.9)

Algorithm (3.9)

 

Time = 17.700 s

Time = 14.223 s

n

\(\|u_{n+1}\|\)

\(\|v_{n+1}\|\)

\(\|u_{n+1}\|\)

\(\|v_{n+1}\|\)

1

1.2997

0.8496

0.8985

0.7560

2

0.6109

1.8814

0.4550

1.5637

3

1.4480

0.4603

0.9682

0.2581

4

0.4061

1.3936

0.4318

1.0630

5

1.1624

0.7364

0.8631

0.7177

6

0.7735

1.1298

0.7839

0.9367

7

1.0413

0.9851

0.9025

0.9110

8

0.9748

1.0935

0.9261

0.9713

9

1.0519

1.0873

0.9713

0.9977

10

1.0611

1.1242

1.0002

1.0301